how can we convert nanometers into eV(electron volt)?? pls explain with help of an example??

To convert nanometers (nm) into electron volts (eV), we need to understand the relationship between wavelength and energy. The energy of a photon can be calculated using the formula derived from Planck's equation, which relates energy to wavelength. Let's break this down step by step.

Understanding the Relationship

The energy (E) of a photon is inversely proportional to its wavelength (λ). This relationship is expressed by the formula:

E = \(\frac{hc}{\lambda}\)

Where:

• E = energy in joules
• h = Planck's constant (approximately \(6.626 \times 10^{-34} \, \text{Js}\))
• c = speed of light (approximately \(3.00 \times 10^8 \, \text{m/s}\))
• λ = wavelength in meters

Converting Wavelength from Nanometers to Meters

Since the wavelength is often given in nanometers, we first need to convert nanometers to meters. Remember that:

1 nm = \(1 \times 10^{-9}\) m

So, if you have a wavelength of, say, 500 nm, you would convert it to meters like this:

500 nm = \(500 \times 10^{-9}\) m = \(5.00 \times 10^{-7}\) m

Calculating Energy in Joules

Now, we can plug this value into the energy formula. Using the constants for Planck's constant and the speed of light:

E = \(\frac{(6.626 \times 10^{-34} \, \text{Js})(3.00 \times 10^8 \, \text{m/s})}{5.00 \times 10^{-7} \, \text{m}}\)

Calculating this gives:

E ≈ \(3.98 \times 10^{-19}\) joules

Converting Joules to Electron Volts

To convert joules to electron volts, we use the conversion factor:

1 eV = \(1.602 \times 10^{-19}\) joules

Now, we can convert the energy we calculated:

E (in eV) = \(\frac{3.98 \times 10^{-19} \, \text{J}}{1.602 \times 10^{-19} \, \text{J/eV}}\)

This results in:

E ≈ 2.48 eV

Summary of the Process

To summarize, the steps to convert nanometers to electron volts are:

• Convert the wavelength from nanometers to meters.
• Use the formula \(E = \frac{hc}{\lambda}\) to find the energy in joules.
• Convert joules to electron volts using the conversion factor.

So, for a wavelength of 500 nm, the energy is approximately 2.48 eV. This process can be applied to any wavelength to find its corresponding energy in electron volts.